Heat oven to 400° F. Toss the squash, oil, and ¼ teaspoon each salt and pepper on a rimmed baking sheet. Roast, turning once, until tender, 35 to 45 minutes.
Brown the bacon in a large nonstick skillet over medium heat, 6 to 8 minutes; remove and crumble. Reserve the skillet.
Add the eggs to the drippings in the skillet and cook, covered, 2 to 4 minutes for slightly runny yolks. Season with ¼ teaspoon pepper.
Serve the squash with the eggs, bacon, and avocado.

Heat oil in a large saucepan over medium heat. Add onion and cook, stirring often, until softened, 2 to 3 minutes. Add broth, water, barley and squash; bring to a simmer, reduce heat to medium-low and simmer until the barley and squash are tender and most of the liquid has been absorbed, about 45 minutes. Add parsley, lemon zest, lemon juice, garlic, salt and pepper; mix gently.